When I tell someone I am a mathematician, one of the most curious common reactions is: “I really liked math class because everything was either right or wrong. There is no ambiguity or doubt.” I ...

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...

Lashi Bandara is affiliated with Australian National University. These are questions I’m often confronted with when people discover I do pure mathematics. I always manage to provide an answer but it ...

Every day, dozens of like-minded mathematicians gather on an online forum called Zulip to build what they believe is the future of their field. They’re all devotees of a software program called Lean.

Tom Oliver does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

Think too hard about it, and mathematics starts to seem like a mighty queer business. For example, are new mathematical truths discovered or invented? Seems like a simple enough question, but for ...

Kurt Gödel's incompleteness theorem demonstrates that mathematics contains true statements that cannot be proved. His proof achieves this by constructing paradoxical mathematical statements. To see ...